- #1

jumboopizza

- 13

- 0

## Homework Statement

the question is simply asking to prove that if speed is constant than velocity and acceleration vectors are perpendicular to each other. it also says as hint to differentiate v dot v= u^2...

V=velocity A=acceleration u=speed t=time

## Homework Equations

i suppose knowing the vector dot product properties would be useful to have around,so here's some:

V dot V= [v]^2(magnitude)

derivative of vector dot products:

d(a dot b)/du= da/du dot b+ a.db/du

acceleration is= the derivative of Velocity with respect to time

## The Attempt at a Solution

ok so I've used the hint and tried to differentiate V dot V= u^2 and i get

dv/dt dot V+V dot dv/dt= du/dt u^2= 0 since speed is constant

2V dot dv/dt=0

now I am not sure if this is representinvg acceleration or not the 2v dv/dt or if its the rate of change in speed or whatever, if its acceleration then wouldn't it be 2A=0, but now it doesn't make sense since acceleration can't be 0 so i know there's a mistake somewhere...

my other idea was to use V dot V=[V]^2 which is one of the dot product properties

and then the magnitude of the velocity would be the speed wouldn't it?

dv/dt [V]^2=0

anyways I am lost,so can someone please help?